Break the eggs into a bowl and beat them with the sugar. Add the yoghurt, oil, flour with baking powder and vanilla sugar and stir until homogeneous.
In an oven dish laid out with baking paper, pour in 1/2 of the dough and bake. In the meantime, boil the vanilla pudding as indicated on the package (it needs to be thicker than usual so it doesn't run).
Once the cake layer is baked, pour the still warm cream over it and on top of it - the rest of the dough.
Bake until ready. Sprinkle with powdered sugar.